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arXiv · 2109.03098

Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form

S. Bandyopadhyay·B. Dacorogna·V. S. Matveev·M. Troyanov
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Abstract

We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0,2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.

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S. Bandyopadhyay, B. Dacorogna, V. S. Matveev, M. Troyanov. 2021-09-07. Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form. https://doi.org/10.1007/s00209-023-03335-1

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